{"id":263,"date":"2026-01-30T23:00:10","date_gmt":"2026-01-30T23:00:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/linear-functions-get-stronger-key-precalculus-practice-page-answer-keys\/"},"modified":"2026-01-30T23:02:45","modified_gmt":"2026-01-30T23:02:45","slug":"linear-functions-get-stronger-key-precalculus-practice-page-answer-keys","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/linear-functions-get-stronger-key-precalculus-practice-page-answer-keys\/","title":{"raw":"Linear Functions: Get Stronger Key -- Precalculus Practice Page Answer Keys","rendered":"Linear Functions: Get Stronger Key — Precalculus Practice Page Answer Keys"},"content":{"raw":"\n\n\t\t
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<\/p>\n\t\t

Linear Functions: Get Stronger Key<\/h1>\n\t\t\t\t\t\t\t\t<\/div>\n\t
\n\t\t\t\t

Linear Functions<\/h2>

1. Terry starts at an elevation of 3000 feet and descends 70 feet per second.<\/p>

3. 3 miles per hour<\/p>

5. [latex]d\\left(t\\right)=100 - 10t[\/latex]<\/p>

7. Yes.<\/p>

9. No.<\/p>

11. No.<\/p>

13. No.<\/p>

15. Increasing.<\/p>

17. Decreasing.<\/p>

19. Decreasing.<\/p>

21. Increasing.<\/p>

23. Decreasing.<\/p>

25. 3<\/p>

27. [latex]-\\frac{1}{3}[\/latex]<\/p>

29. [latex]\\frac{4}{5}[\/latex]<\/p>

31. [latex]f\\left(x\\right)=-\\frac{1}{2}x+\\frac{7}{2}[\/latex]<\/p>

33. [latex]y=2x+3[\/latex]<\/p>

35. [latex]y=-\\frac{1}{3}x+\\frac{22}{3}[\/latex]<\/p>

37. [latex]y=\\frac{4}{5}x+4[\/latex]<\/p>

39. [latex]-\\frac{5}{4}[\/latex]<\/p>

41. [latex]y=\\frac{2}{3}x+1[\/latex]<\/p>

43. [latex]y=-2x+3[\/latex]<\/p>

45. [latex]y=3[\/latex]<\/p>

47. Linear, [latex]g\\left(x\\right)=-3x+5[\/latex]<\/p>

49. Linear, [latex]f\\left(x\\right)=5x - 5[\/latex]<\/p>

51. Linear, [latex]g\\left(x\\right)=-\\frac{25}{2}x+6[\/latex]<\/p>

53. Linear, [latex]f\\left(x\\right)=10x - 24[\/latex]<\/p>

55. [latex]f\\left(x\\right)=-58x+17.3[\/latex]<\/p>

57.
\"\"<\/p>

59. a. [latex]a=11,900[\/latex] ; [latex]b=1001.1[\/latex] b. [latex]q\\left(p\\right)=1000p - 100[\/latex]<\/p>

61.
\"..\"<\/p>

63. [latex]x=-\\frac{16}{3}[\/latex]<\/p>

65. [latex]x=a[\/latex]<\/p>

67. [latex]y=\\frac{d}{c-a}x-\\frac{ad}{c-a}[\/latex]<\/p>

69. $45 per training session.<\/p>

71. The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.<\/p>

73. The slope is \u2013400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.<\/p>

75. c<\/p>

Graphs of Linear Functions<\/h2>

1. The slopes are equal; y-intercepts are not equal.<\/p>

3. The point of intersection is [latex]\\left(a,a\\right)[\/latex]. This is because for the horizontal line, all of the y<\/em> coordinates are a<\/em> and for the vertical line, all of the x<\/em> coordinates are a<\/em>. The point of intersection will have these two characteristics.<\/p>

5. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation [latex]y=mx+b[\/latex] and solve for b<\/em>. Then write the equation of the line in the form [latex]y=mx+b[\/latex] by substituting in m<\/em> and b<\/em>.<\/p>

7. neither parallel or perpendicular<\/p>

9. perpendicular<\/p>

11. parallel<\/p>

13. [latex]\\left(-2\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 4}\\right)[\/latex]<\/p>

15. [latex]\\left(\\frac{1}{5}\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 1}\\right)[\/latex]<\/p>

17. [latex]\\left(8\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, }28\\right)[\/latex]<\/p>

19. [latex]\\text{Line 1}: m=8 \\text{ Line 2}: m=-6 \\text{Neither}[\/latex]<\/p>

21. [latex]\\text{Line 1}: m=-\\frac{1}{2} \\text{ Line 2}: m=2 \\text{Perpendicular}[\/latex]<\/p>

23. [latex]\\text{Line 1}: m=-2 \\text{ Line 2}: m=-2 \\text{Parallel}[\/latex]<\/p>

25. [latex]g\\left(x\\right)=3x - 3[\/latex]<\/p>

27. [latex]p\\left(t\\right)=-\\frac{1}{3}t+2[\/latex]<\/p>

29. [latex]\\left(-2,1\\right)[\/latex]<\/p>

31. [latex]\\left(-\\frac{17}{5},\\frac{5}{3}\\right)[\/latex]<\/p>

33. F<\/p>

35. C<\/p>

37. A<\/p>

39.
\"\"<\/p>

41.
\"\"<\/p>

43.
\"\"<\/p>

45.
\"\"<\/p>

47.
\"\"<\/p>

49.
\"\"<\/p>

51.
\"\"<\/p>

53.
\"\"<\/p>

55.
\"\"<\/p>

57.
\"\"<\/p>

59. [latex]g\\left(x\\right)=0.75x - 5.5\\text{}[\/latex] 0.75 [latex]\\left(0,-5.5\\right)[\/latex]<\/p>

61. [latex]y=3[\/latex]<\/p>

63. [latex]x=-3[\/latex]<\/p>

65. no point of intersection<\/p>

67. [latex]\\left(\\text{2},\\text{ 7}\\right)[\/latex]<\/p>

69. [latex]\\left(-10,\\text{ }-5\\right)[\/latex]<\/p>

71. [latex]y=100x - 98[\/latex]<\/p>

73. [latex]x<\\frac{1999}{201}x>\\frac{1999}{201}[\/latex]<\/p>

75. Less than 3000 texts<\/p>

Modeling with Linear Functions<\/h2>

1. Determine the independent variable. This is the variable upon which the output depends.<\/p>

3. To determine the initial value, find the output when the input is equal to zero.<\/p>

5. 6 square units<\/p>

7. 20.012 square units<\/p>

9. 2,300<\/p>

11. 64,170<\/p>

13. [latex]P\\left(t\\right)=75,000+2500t[\/latex]<\/p>

15. (\u201330, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.<\/p>

17. Ten years after the model began.<\/p>

19. [latex]W\\left(t\\right)=\\text{7}.\\text{5}t+0.\\text{5}[\/latex]<\/p>

21. (\u201315, 0): The x-intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. (0, 7.5): The baby weighed 7.5 pounds at birth.<\/p>

23. At age 5.8 months.<\/p>

25. [latex]C\\left(t\\right)=12,025 - 205t[\/latex]<\/p>

27. (58.7, 0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0, 12,025): Initially there were 12,025 people afflicted by the common cold.<\/p>

29. 2064<\/p>

31. [latex]y=-2t+180[\/latex]<\/p>

33. In 2070, the company\u2019s profit will be zero.<\/p>

35. [latex]y=30t - 300[\/latex]<\/p>

37. (10, 0) In 1990, the profit earned zero profit.<\/p>

39. Hawaii<\/p>

41. During the year 1933<\/p>

43. $105,620<\/p>

45.<\/p>

a. 696 people
b. 4 years
c. 174 people per year
d. 305 people
e. [latex]P\\left(t\\right)=305+174t[\/latex]
f. 2219 people<\/p>

47.<\/p>

a. [latex]C\\left(x\\right)=0.15x+10[\/latex]
b. The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
c. $113.05<\/p>

49.<\/p>

a. [latex]P\\left(t\\right)=190t+4360[\/latex]
b. 6640 moose<\/p>

51.<\/p>

a. [latex]R\\left(t\\right)=16 - 2.1t[\/latex]
b. 5.5 billion cubic feet
c. During the year 2017<\/p>

53. More than 133 minutes<\/p>

55. More than $42,857.14 worth of jewelry<\/p>

57. $66,666.67<\/p>

Fitting Linear Models to Data<\/h2>

1. When our model no longer applies, after some value in the domain, the model itself doesn\u2019t hold.<\/p>

3. We predict a value outside the domain and range of the data.<\/p>

5. The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.<\/p>

7. 61.966 years<\/p>

9. No<\/p>

11. No<\/p>

13. Interpolation. About [latex]60^\\circ \\text{ F}[\/latex].<\/p>

15. C<\/p>

17. B<\/p>

19.
\"\"<\/p>

21.
\"\"<\/p>

23. Yes, trend appears linear because [latex]r=0.\\text{985}[\/latex] and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.<\/p>

25. [latex]y=\\text{1}.\\text{64}0x+\\text{13}.\\text{8}00[\/latex] , [latex]r=0.\\text{987}[\/latex]<\/p>

27. [latex]y=-0.962x+26.86, r=-0.965[\/latex]<\/p>

29. [latex]y=-\\text{1}.\\text{981}x+\\text{6}0.\\text{197}[\/latex] ; [latex]r=-0.\\text{998}[\/latex]<\/p>

31. [latex]y=0.\\text{121}x - 38.841,r=0.998[\/latex]<\/p>

33. [latex]\\left(-2,\\text{ }-6\\right),\\left(1,\\text{ }-12\\right),\\left(5,\\text{ }-20\\right),\\left(6,\\text{ }-22\\right),\\left(9,\\text{ }-28\\right)[\/latex]; [latex]y=-2x - 10[\/latex]<\/p>

35. [latex]\\left(\\text{189}.\\text{8},0\\right)[\/latex] If 18,980 units are sold, the company will have a profit of zero dollars.<\/p>

37. [latex]y=0.00587x+\\text{1985}.4\\text{1}[\/latex]<\/p>

39. [latex]y=\\text{2}0.\\text{25}x-\\text{671}.\\text{5}[\/latex]<\/p>

41. [latex]y=-\\text{1}0.\\text{75}x+\\text{742}.\\text{5}0[\/latex]<\/p>

43. Yes<\/p>

45. Increasing<\/p>

47. [latex]y=-\\text{3}x+\\text{26}[\/latex]<\/p>

49. 3<\/p>

51. [latex]y=\\text{2}x-\\text{2}[\/latex]<\/p>

53. Not linear<\/p>

55. parallel<\/p>

57. [latex]\\left(-9,0\\right);\\left(0,-7\\right)[\/latex]<\/p>

59. Line 1: [latex]m=-2[\/latex]; Line 2: [latex]m=-2[\/latex]; Parallel<\/p>

61. [latex]y=-0.2x+21[\/latex]<\/p>

63.
\"\"<\/p>

65. 250<\/p>

67. 118,000<\/p>

69. [latex]y=-\\text{3}00x+\\text{11},\\text{5}00[\/latex]<\/p>

71. a) 800 b) 100 students per year c) [latex]P\\left(t\\right)=100t+1700[\/latex]<\/p>

73. 18,500<\/p>

75. $91,625<\/p>

77. Extrapolation.
\"\"<\/p>

79.
\"\"<\/p>

81. Midway through 2024<\/p>

83. [latex]y=-1.294x+49.412;\\text{ } r=-0.974[\/latex]<\/p>

85. Early in 2022<\/p>

87. 7,660<\/p>

Absolute Value Functions<\/h2>

1. Isolate the absolute value term so that the equation is of the form [latex]|A|=B[\/latex]. Form one equation by setting the expression inside the absolute value symbol, [latex]A[\/latex], equal to the expression on the other side of the equation, [latex]B[\/latex]. Form a second equation by setting [latex]A[\/latex] equal to the opposite of the expression on the other side of the equation, -B. Solve each equation for the variable.<\/span><\/p>

3. The graph of the absolute value function does not cross the [latex]x[\/latex] -axis, so the graph is either completely above or completely below the [latex]x[\/latex] -axis.<\/span><\/p>

5. First determine the boundary points by finding the solution(s) of the equation. Use the boundary points to form possible solution intervals. Choose a test value in each interval to determine which values satisfy the inequality.<\/span><\/p>

7. [latex]|x+4|=\\frac{1}{2}[\/latex]<\/span><\/p>

9. [latex]|f\\left(x\\right)-8|<0.03[\/latex]<\/span><\/span><\/p>

11. [latex]\\left\\{1,11\\right\\}[\/latex]<\/span><\/p>

13. [latex]\\left\\{\\frac{9}{4},\\frac{13}{4}\\right\\}[\/latex]<\/span><\/p>

15. [latex]\\left\\{\\frac{10}{3},\\frac{20}{3}\\right\\}[\/latex]<\/span><\/p>

17. [latex]\\left\\{\\frac{11}{5},\\frac{29}{5}\\right\\}[\/latex]<\/span><\/p>

19. [latex]\\left\\{\\frac{5}{2},\\frac{7}{2}\\right\\}[\/latex]<\/span><\/p>

21. No solution<\/span><\/p>

23. [latex]\\left\\{-57,27\\right\\}[\/latex]<\/span><\/p>

25. [latex]\\left(0,-8\\right);\\left(-6,0\\right),\\left(4,0\\right)[\/latex]<\/span><\/p>

27. [latex]\\left(0,-7\\right)[\/latex]; no [latex]x[\/latex] -intercepts<\/span><\/p>

29. [latex]\\left(-\\infty ,-8\\right)\\cup \\left(12,\\infty \\right)[\/latex]<\/span><\/p>

31. [latex]\\frac{-4}{3}\\le x\\le 4[\/latex]<\/span><\/p>

33. [latex]\\left(-\\infty ,-\\frac{8}{3}\\right]\\cup \\left[6,\\infty \\right)[\/latex]<\/span><\/p>

35. [latex]\\left(-\\infty ,-\\frac{8}{3}\\right]\\cup \\left[16,\\infty \\right)[\/latex]<\/span><\/p>

37.
\"Graph<\/p>

39.
\"Graph<\/p>

41.
\"Graph<\/p>

43.
\"Graph<\/p>

45.
\"Graph<\/p>

47.
\"Graph<\/p>

49.
\"Graph<\/p>

51.
\"Graph<\/p>

53. range: [latex]\\left[0,20\\right][\/latex]
\"Graph<\/p>

55. [latex]x\\text{-}[\/latex] intercepts:
\"Graph<\/p>

57. [latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>

59. There is no solution for [latex]a[\/latex] that will keep the function from having a [latex]y[\/latex] -intercept. The absolute value function always crosses the [latex]y[\/latex] -intercept when [latex]x=0[\/latex].<\/p>

61. [latex]|p - 0.08|\\le 0.015[\/latex]<\/p>

63. [latex]|x - 5.0|\\le 0.01[\/latex]<\/p> \n\t<\/div>\n\t\t\t\n\t\t\t<\/div>\n\n\t\t<\/div>\n\t\n","rendered":"

\n
\n
\n

\n

Linear Functions: Get Stronger Key<\/h1>\n<\/p><\/div>\n
\n

Linear Functions<\/h2>\n

1. Terry starts at an elevation of 3000 feet and descends 70 feet per second.<\/p>\n

3. 3 miles per hour<\/p>\n

5. [latex]d\\left(t\\right)=100 - 10t[\/latex]<\/p>\n

7. Yes.<\/p>\n

9. No.<\/p>\n

11. No.<\/p>\n

13. No.<\/p>\n

15. Increasing.<\/p>\n

17. Decreasing.<\/p>\n

19. Decreasing.<\/p>\n

21. Increasing.<\/p>\n

23. Decreasing.<\/p>\n

25. 3<\/p>\n

27. [latex]-\\frac{1}{3}[\/latex]<\/p>\n

29. [latex]\\frac{4}{5}[\/latex]<\/p>\n

31. [latex]f\\left(x\\right)=-\\frac{1}{2}x+\\frac{7}{2}[\/latex]<\/p>\n

33. [latex]y=2x+3[\/latex]<\/p>\n

35. [latex]y=-\\frac{1}{3}x+\\frac{22}{3}[\/latex]<\/p>\n

37. [latex]y=\\frac{4}{5}x+4[\/latex]<\/p>\n

39. [latex]-\\frac{5}{4}[\/latex]<\/p>\n

41. [latex]y=\\frac{2}{3}x+1[\/latex]<\/p>\n

43. [latex]y=-2x+3[\/latex]<\/p>\n

45. [latex]y=3[\/latex]<\/p>\n

47. Linear, [latex]g\\left(x\\right)=-3x+5[\/latex]<\/p>\n

49. Linear, [latex]f\\left(x\\right)=5x - 5[\/latex]<\/p>\n

51. Linear, [latex]g\\left(x\\right)=-\\frac{25}{2}x+6[\/latex]<\/p>\n

53. Linear, [latex]f\\left(x\\right)=10x - 24[\/latex]<\/p>\n

55. [latex]f\\left(x\\right)=-58x+17.3[\/latex]<\/p>\n

57.
\"\"<\/p>\n

59. a. [latex]a=11,900[\/latex] ; [latex]b=1001.1[\/latex] b. [latex]q\\left(p\\right)=1000p - 100[\/latex]<\/p>\n

61.
\"..\"<\/p>\n

63. [latex]x=-\\frac{16}{3}[\/latex]<\/p>\n

65. [latex]x=a[\/latex]<\/p>\n

67. [latex]y=\\frac{d}{c-a}x-\\frac{ad}{c-a}[\/latex]<\/p>\n

69. $45 per training session.<\/p>\n

71. The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.<\/p>\n

73. The slope is \u2013400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.<\/p>\n

75. c<\/p>\n

Graphs of Linear Functions<\/h2>\n

1. The slopes are equal; y-intercepts are not equal.<\/p>\n

3. The point of intersection is [latex]\\left(a,a\\right)[\/latex]. This is because for the horizontal line, all of the y<\/em> coordinates are a<\/em> and for the vertical line, all of the x<\/em> coordinates are a<\/em>. The point of intersection will have these two characteristics.<\/p>\n

5. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation [latex]y=mx+b[\/latex] and solve for b<\/em>. Then write the equation of the line in the form [latex]y=mx+b[\/latex] by substituting in m<\/em> and b<\/em>.<\/p>\n

7. neither parallel or perpendicular<\/p>\n

9. perpendicular<\/p>\n

11. parallel<\/p>\n

13. [latex]\\left(-2\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 4}\\right)[\/latex]<\/p>\n

15. [latex]\\left(\\frac{1}{5}\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 1}\\right)[\/latex]<\/p>\n

17. [latex]\\left(8\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, }28\\right)[\/latex]<\/p>\n

19. [latex]\\text{Line 1}: m=8 \\text{ Line 2}: m=-6 \\text{Neither}[\/latex]<\/p>\n

21. [latex]\\text{Line 1}: m=-\\frac{1}{2} \\text{ Line 2}: m=2 \\text{Perpendicular}[\/latex]<\/p>\n

23. [latex]\\text{Line 1}: m=-2 \\text{ Line 2}: m=-2 \\text{Parallel}[\/latex]<\/p>\n

25. [latex]g\\left(x\\right)=3x - 3[\/latex]<\/p>\n

27. [latex]p\\left(t\\right)=-\\frac{1}{3}t+2[\/latex]<\/p>\n

29. [latex]\\left(-2,1\\right)[\/latex]<\/p>\n

31. [latex]\\left(-\\frac{17}{5},\\frac{5}{3}\\right)[\/latex]<\/p>\n

33. F<\/p>\n

35. C<\/p>\n

37. A<\/p>\n

39.
\"\"<\/p>\n

41.
\"\"<\/p>\n

43.
\"\"<\/p>\n

45.
\"\"<\/p>\n

47.
\"\"<\/p>\n

49.
\"\"<\/p>\n

51.
\"\"<\/p>\n

53.
\"\"<\/p>\n

55.
\"\"<\/p>\n

57.
\"\"<\/p>\n

59. [latex]g\\left(x\\right)=0.75x - 5.5\\text{}[\/latex] 0.75 [latex]\\left(0,-5.5\\right)[\/latex]<\/p>\n

61. [latex]y=3[\/latex]<\/p>\n

63. [latex]x=-3[\/latex]<\/p>\n

65. no point of intersection<\/p>\n

67. [latex]\\left(\\text{2},\\text{ 7}\\right)[\/latex]<\/p>\n

69. [latex]\\left(-10,\\text{ }-5\\right)[\/latex]<\/p>\n

71. [latex]y=100x - 98[\/latex]<\/p>\n

73. [latex]x<\\frac{1999}{201}x>\\frac{1999}{201}[\/latex]<\/p>\n

75. Less than 3000 texts<\/p>\n

Modeling with Linear Functions<\/h2>\n

1. Determine the independent variable. This is the variable upon which the output depends.<\/p>\n

3. To determine the initial value, find the output when the input is equal to zero.<\/p>\n

5. 6 square units<\/p>\n

7. 20.012 square units<\/p>\n

9. 2,300<\/p>\n

11. 64,170<\/p>\n

13. [latex]P\\left(t\\right)=75,000+2500t[\/latex]<\/p>\n

15. (\u201330, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.<\/p>\n

17. Ten years after the model began.<\/p>\n

19. [latex]W\\left(t\\right)=\\text{7}.\\text{5}t+0.\\text{5}[\/latex]<\/p>\n

21. (\u201315, 0): The x-intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. (0, 7.5): The baby weighed 7.5 pounds at birth.<\/p>\n

23. At age 5.8 months.<\/p>\n

25. [latex]C\\left(t\\right)=12,025 - 205t[\/latex]<\/p>\n

27. (58.7, 0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0, 12,025): Initially there were 12,025 people afflicted by the common cold.<\/p>\n

29. 2064<\/p>\n

31. [latex]y=-2t+180[\/latex]<\/p>\n

33. In 2070, the company\u2019s profit will be zero.<\/p>\n

35. [latex]y=30t - 300[\/latex]<\/p>\n

37. (10, 0) In 1990, the profit earned zero profit.<\/p>\n

39. Hawaii<\/p>\n

41. During the year 1933<\/p>\n

43. $105,620<\/p>\n

45.<\/p>\n

a. 696 people
b. 4 years
c. 174 people per year
d. 305 people
e. [latex]P\\left(t\\right)=305+174t[\/latex]
f. 2219 people<\/p>\n

47.<\/p>\n

a. [latex]C\\left(x\\right)=0.15x+10[\/latex]
b. The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
c. $113.05<\/p>\n

49.<\/p>\n

a. [latex]P\\left(t\\right)=190t+4360[\/latex]
b. 6640 moose<\/p>\n

51.<\/p>\n

a. [latex]R\\left(t\\right)=16 - 2.1t[\/latex]
b. 5.5 billion cubic feet
c. During the year 2017<\/p>\n

53. More than 133 minutes<\/p>\n

55. More than $42,857.14 worth of jewelry<\/p>\n

57. $66,666.67<\/p>\n

Fitting Linear Models to Data<\/h2>\n

1. When our model no longer applies, after some value in the domain, the model itself doesn\u2019t hold.<\/p>\n

3. We predict a value outside the domain and range of the data.<\/p>\n

5. The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.<\/p>\n

7. 61.966 years<\/p>\n

9. No<\/p>\n

11. No<\/p>\n

13. Interpolation. About [latex]60^\\circ \\text{ F}[\/latex].<\/p>\n

15. C<\/p>\n

17. B<\/p>\n

19.
\"\"<\/p>\n

21.
\"\"<\/p>\n

23. Yes, trend appears linear because [latex]r=0.\\text{985}[\/latex] and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.<\/p>\n

25. [latex]y=\\text{1}.\\text{64}0x+\\text{13}.\\text{8}00[\/latex] , [latex]r=0.\\text{987}[\/latex]<\/p>\n

27. [latex]y=-0.962x+26.86, r=-0.965[\/latex]<\/p>\n

29. [latex]y=-\\text{1}.\\text{981}x+\\text{6}0.\\text{197}[\/latex] ; [latex]r=-0.\\text{998}[\/latex]<\/p>\n

31. [latex]y=0.\\text{121}x - 38.841,r=0.998[\/latex]<\/p>\n

33. [latex]\\left(-2,\\text{ }-6\\right),\\left(1,\\text{ }-12\\right),\\left(5,\\text{ }-20\\right),\\left(6,\\text{ }-22\\right),\\left(9,\\text{ }-28\\right)[\/latex]; [latex]y=-2x - 10[\/latex]<\/p>\n

35. [latex]\\left(\\text{189}.\\text{8},0\\right)[\/latex] If 18,980 units are sold, the company will have a profit of zero dollars.<\/p>\n

37. [latex]y=0.00587x+\\text{1985}.4\\text{1}[\/latex]<\/p>\n

39. [latex]y=\\text{2}0.\\text{25}x-\\text{671}.\\text{5}[\/latex]<\/p>\n

41. [latex]y=-\\text{1}0.\\text{75}x+\\text{742}.\\text{5}0[\/latex]<\/p>\n

43. Yes<\/p>\n

45. Increasing<\/p>\n

47. [latex]y=-\\text{3}x+\\text{26}[\/latex]<\/p>\n

49. 3<\/p>\n

51. [latex]y=\\text{2}x-\\text{2}[\/latex]<\/p>\n

53. Not linear<\/p>\n

55. parallel<\/p>\n

57. [latex]\\left(-9,0\\right);\\left(0,-7\\right)[\/latex]<\/p>\n

59. Line 1: [latex]m=-2[\/latex]; Line 2: [latex]m=-2[\/latex]; Parallel<\/p>\n

61. [latex]y=-0.2x+21[\/latex]<\/p>\n

63.
\"\"<\/p>\n

65. 250<\/p>\n

67. 118,000<\/p>\n

69. [latex]y=-\\text{3}00x+\\text{11},\\text{5}00[\/latex]<\/p>\n

71. a) 800 b) 100 students per year c) [latex]P\\left(t\\right)=100t+1700[\/latex]<\/p>\n

73. 18,500<\/p>\n

75. $91,625<\/p>\n

77. Extrapolation.
\"\"<\/p>\n

79.
\"\"<\/p>\n

81. Midway through 2024<\/p>\n

83. [latex]y=-1.294x+49.412;\\text{ } r=-0.974[\/latex]<\/p>\n

85. Early in 2022<\/p>\n

87. 7,660<\/p>\n

Absolute Value Functions<\/h2>\n

1. Isolate the absolute value term so that the equation is of the form [latex]|A|=B[\/latex]. Form one equation by setting the expression inside the absolute value symbol, [latex]A[\/latex], equal to the expression on the other side of the equation, [latex]B[\/latex]. Form a second equation by setting [latex]A[\/latex] equal to the opposite of the expression on the other side of the equation, -B. Solve each equation for the variable.<\/span><\/p>\n

3. The graph of the absolute value function does not cross the [latex]x[\/latex] -axis, so the graph is either completely above or completely below the [latex]x[\/latex] -axis.<\/span><\/p>\n

5. First determine the boundary points by finding the solution(s) of the equation. Use the boundary points to form possible solution intervals. Choose a test value in each interval to determine which values satisfy the inequality.<\/span><\/p>\n

7. [latex]|x+4|=\\frac{1}{2}[\/latex]<\/span><\/p>\n

9. [latex]|f\\left(x\\right)-8|<0.03[\/latex]<\/span><\/span><\/p>\n

11. [latex]\\left\\{1,11\\right\\}[\/latex]<\/span><\/p>\n

13. [latex]\\left\\{\\frac{9}{4},\\frac{13}{4}\\right\\}[\/latex]<\/span><\/p>\n

15. [latex]\\left\\{\\frac{10}{3},\\frac{20}{3}\\right\\}[\/latex]<\/span><\/p>\n

17. [latex]\\left\\{\\frac{11}{5},\\frac{29}{5}\\right\\}[\/latex]<\/span><\/p>\n

19. [latex]\\left\\{\\frac{5}{2},\\frac{7}{2}\\right\\}[\/latex]<\/span><\/p>\n

21. No solution<\/span><\/p>\n

23. [latex]\\left\\{-57,27\\right\\}[\/latex]<\/span><\/p>\n

25. [latex]\\left(0,-8\\right);\\left(-6,0\\right),\\left(4,0\\right)[\/latex]<\/span><\/p>\n

27. [latex]\\left(0,-7\\right)[\/latex]; no [latex]x[\/latex] -intercepts<\/span><\/p>\n

29. [latex]\\left(-\\infty ,-8\\right)\\cup \\left(12,\\infty \\right)[\/latex]<\/span><\/p>\n

31. [latex]\\frac{-4}{3}\\le x\\le 4[\/latex]<\/span><\/p>\n

33. [latex]\\left(-\\infty ,-\\frac{8}{3}\\right]\\cup \\left[6,\\infty \\right)[\/latex]<\/span><\/p>\n

35. [latex]\\left(-\\infty ,-\\frac{8}{3}\\right]\\cup \\left[16,\\infty \\right)[\/latex]<\/span><\/p>\n

37.
\"Graph<\/p>\n

39.
\"Graph<\/p>\n

41.
\"Graph<\/p>\n

43.
\"Graph<\/p>\n

45.
\"Graph<\/p>\n

47.
\"Graph<\/p>\n

49.
\"Graph<\/p>\n

51.
\"Graph<\/p>\n

53. range: [latex]\\left[0,20\\right][\/latex]
\"Graph<\/p>\n

55. [latex]x\\text{-}[\/latex] intercepts:
\"Graph<\/p>\n

57. [latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>\n

59. There is no solution for [latex]a[\/latex] that will keep the function from having a [latex]y[\/latex] -intercept. The absolute value function always crosses the [latex]y[\/latex] -intercept when [latex]x=0[\/latex].<\/p>\n

61. [latex]|p - 0.08|\\le 0.015[\/latex]<\/p>\n

63. [latex]|x - 5.0|\\le 0.01[\/latex]<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n","protected":false},"author":13,"menu_order":3,"template":"","meta":{"_candela_citation":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":224,"module-header":"","content_attributions":null,"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/revisions"}],"predecessor-version":[{"id":295,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/revisions\/295"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/224"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=263"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=263"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=263"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}